Derousseau's Generalization of the Malfatti circles

\(a:b:c=5:12:13\).

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[Other solutions]
[Guy]
[Lob & Richmond]

\(\mathbf{5}\) \((202)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&0.915631799079&{}:{}&0.040496736442&{}:{}&0.043871464479&,\\B^\prime&{}\approx{}&0.823111595205&{}:{}&-1.963201742740&{}:{}&2.140090147534&,\\C^\prime&{}\approx{}&0.698502526124&{}:{}&1.676406062698&{}:{}&-1.374908588822&. \end{alignedat} \]
5 (202)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}0.101241841105\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}4.938669571233\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}4.191015156744\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.166666666667&{}:{}&0.400000000000&{}:{}&0.433333333333&. \end{alignedat} \]
5 (202)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.834847233084&{}:{}&0.021238066511&{}:{}&0.143914700405&. \end{alignedat} \]
5 (202)

Hiroyasu Kamo